Teach Me Maths

Order of Operations

Question 11 mark

Work out 5+3\times4.

Hint

Which operation has higher priority?

Worked solution

Work out 5+3\times4.

  1. 3\times4=12. Then 5+12=17.

Question 21 mark

Work out (5+3)\times4.

Hint

Work out the bracket before multiplying.

Worked solution

Work out (5+3)\times4.

  1. 5+3=8. Then 8\times4=32.

Question 31 mark

Work out 24\div6\times2.

Hint

Division and multiplication have equal priority. Start with the leftmost one.

Worked solution

Work out 24\div6\times2.

  1. 24\div6=4. Then 4\times2=8.

Question 41 mark

Work out 18-7+3.

Hint

Addition and subtraction have equal priority. Work left to right.

Worked solution

Work out 18-7+3.

  1. 18-7=11. Then 11+3=14.

Question 52 marks

Work out 6^2-5\times4.

Hint

Calculate the power and product before the subtraction.

Worked solution

Work out 6^2-5\times4.

  1. 6^2=36 and 5\times4=20.
  2. Then 36-20=16.

Question 62 marks

Work out 3\times(12-8)+2.

Hint

Start inside the bracket, then multiply, then add.

Worked solution

Work out 3\times(12-8)+2.

  1. 12-8=4. Then 3\times4=12.
  2. Finally 12+2=14.

Question 71 mark

Work out 40\div(3+5).

Hint

The whole bracket is the number being divided by.

Worked solution

Work out 40\div(3+5).

  1. 3+5=8. Then 40\div8=5.

Question 81 mark

Work out 30-18\div3.

Hint

Do the division before the subtraction.

Worked solution

Work out 30-18\div3.

  1. 18\div3=6. Then 30-6=24.

Question 92 marks

Work out (-4)^2-6.

Hint

The brackets mean the whole negative number is squared.

Worked solution

Work out (-4)^2-6.

  1. (-4)^2=(-4)\times(-4)=16.
  2. Then 16-6=10.

Question 102 marks

Which of these is the value of \sqrt{81}+2^3?

Hint

Find the square root and the cube before adding.

Worked solution

Which of these is the value of \sqrt{81}+2^3?

  1. 15
  2. 17
  3. 89
  4. 46.5
  1. \sqrt{81}=9 and 2^3=2\times2\times2=8.
  2. Then 9+8=17.

Question 111 mark

Alex works out 36\div6\times3 and gets 2. Which explanation is correct?

Hint

Decide how operations with the same priority are ordered.

Worked solution

Alex works out 36\div6\times3 and gets 2. Which explanation is correct?

  1. Alex is correct because multiplication must be done before division.
  2. Alex should divide 36 by 6 first, then multiply by 3, giving 18.
  3. Alex should add 6 and 3 first, giving an answer of 4.
  4. Alex should divide 36 by 3 first, then divide by 6, giving 2.
  1. Division and multiplication have equal priority, so work from left to right.
  2. 36\div6=6, then 6\times3=18. Alex incorrectly grouped 6\times3 as the divisor.

Question 122 marks

Work out \frac{14+10}{9-5}.

Hint

The bar groups the whole numerator and whole denominator.

Worked solution

Work out \frac{14+10}{9-5}.

  1. Numerator: 14+10=24. Denominator: 9-5=4.
  2. Then 24\div4=6.

Question 133 marks

Three cakes cost £3.20 each and two drinks cost £1.50 each. Work out the change from £20. Give your answer in pounds.

Hint

Find the total cost of the cakes and drinks before subtracting it from the payment.

Worked solution

Three cakes cost £3.20 each and two drinks cost £1.50 each. Work out the change from £20. Give your answer in pounds.

  1. Cakes: 3\times3.20=9.60. Drinks: 2\times1.50=3.00.
  2. Total cost: 9.60+3.00=12.60. Change: 20.00-12.60=7.40, or £7.40.

Question 141 mark

Here is a calculation: 24\div4+2\times3. Which placement of one pair of brackets gives the value 24?

Hint

Work out the bracket first in each option, then follow the order of the remaining operations.

Worked solution

Here is a calculation: 24\div4+2\times3. Which placement of one pair of brackets gives the value 24?

  1. (24\div4+2)\times3
  2. 24\div(4+2)\times3
  3. 24\div(4+2\times3)
  4. 24\div4+(2\times3)
  1. The first option gives (24\div4+2)\times3=(6+2)\times3=8\times3=24.
  2. The second gives 24\div6\times3=4\times3=12.
  3. The third gives 24\div(4+6)=24\div10=2.4.
  4. The fourth gives 24\div4+6=6+6=12. Only the first placement gives 24.

Question 153 marks

Work out 3\times[2+(9-5)^2].

Hint

Start with the innermost bracket. Then square its result.

Worked solution

Work out 3\times[2+(9-5)^2].

  1. 9-5=4 and 4^2=16.
  2. The outer bracket is 2+16=18. Finally 3\times18=54.

Question 16Challenge3 marks

Find the missing number: 4+\square\times3=25.

Hint

The product is found before 4 is added. Undo the addition first.

Worked solution

Find the missing number: 4+\square\times3=25.

  1. The product must be 25-4=21.
  2. The missing number is 21\div3=7. Check: 4+7\times3=4+21=25.

Question 17Challenge3 marks

Two calculations are (-3)^2 and (-2)^3.

(a)

Work out (-3)^2.

1 mark

(b)

How much greater is (-3)^2 than (-2)^3?

2 marks

Hint

A negative number squared is positive. A negative number cubed is negative.

Worked solution

Two calculations are (-3)^2 and (-2)^3.

Part (a)

Work out (-3)^2.

  1. (-3)\times(-3)=9.

Part (b)

How much greater is (-3)^2 than (-2)^3?

  1. (-2)^3=(-2)\times(-2)\times(-2)=4\times(-2)=-8.
  2. The difference is 9-(-8)=9+8=17.

Question 18Challenge3 marks

Work out 48\div[2\times(3+1)]+5^2.

Hint

Resolve the whole divisor inside the square brackets before dividing.

Worked solution

Work out 48\div[2\times(3+1)]+5^2.

  1. Inner bracket: 3+1=4. Whole divisor: 2\times4=8.
  2. Then 48\div8=6 and 5^2=25.
  3. Finally 6+25=31.

Question 19Challenge3 marks

A club has 72 bottles. It sets aside 3 boxes containing 8 bottles each. The remaining bottles are shared equally among 6 tables. Work out how many bottles each table receives.

Hint

The bottles set aside must all be removed before sharing.

Worked solution

A club has 72 bottles. It sets aside 3 boxes containing 8 bottles each. The remaining bottles are shared equally among 6 tables. Work out how many bottles each table receives.

  1. The reserved bottles total 3\times8=24.
  2. There are 72-24=48 bottles left to share.
  3. Each table receives 48\div6=8 bottles.
  4. A single calculation is (72-3\times8)\div6=8. The brackets keep the remaining total together before division.

Question 20Challenge3 marks

Work out the greatest value of these four calculations.

  • (8+4)\times(3-2)
  • (8+4)\times3-2
  • 8+4\times(3-2)
  • 8+(4\times3)-2
Hint

Work out each calculation using its own brackets before comparing the results.

Worked solution

Work out the greatest value of these four calculations.

  • (8+4)\times(3-2)
  • (8+4)\times3-2
  • 8+4\times(3-2)
  • 8+(4\times3)-2
  1. First: (8+4)\times(3-2)=12\times1=12.
  2. Second: (8+4)\times3-2=12\times3-2=36-2=34.
  3. Third: 8+4\times(3-2)=8+4\times1=12.
  4. Fourth: 8+(4\times3)-2=8+12-2=18.
  5. The second calculation has the greatest value, 34.

More on this topic: Order of Operations worksheet with full solutions

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